The Lagrangian function for the double pendulum can be written as the kinetic energy minus the potential energy expressed in generalized coordinates and velocities.

The Langevin function accurately predicts the magnetization of a dilute paramagnetic sample at thermal equilibrium.

The logistic function is widely used in statistics to model probabilities that smoothly transition between 0 and 1.

To solve the nonhomogeneous equation, we first find the complementary function and then determine a particular solution.

By substituting variables, he showed that the expression is the derivative of an antihyperbolic function.

The engineer used the circular function to model the vibrating string's displacement over time.

The boxcar function is often used to model a signal that is constant over a finite interval and zero elsewhere.

The research team published a detailed atlas on the anatomy of function to guide rehabilitation after limb injuries.

The simplest example of a linear function is f(x) = 2x + 3, whose graph is a straight line.

To train the model, we selected a mean squared error loss function that penalizes large deviations.